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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Nov 2012 11:59:14 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/20/t1353430788ztihvz3h3esdvpv.htm/, Retrieved Mon, 29 Apr 2024 18:43:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191186, Retrieved Mon, 29 Apr 2024 18:43:39 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [WS 9 ACF 2] [2012-11-20 16:59:14] [851af2766980873020febd248b5479af] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191186&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191186&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.274566	3.3962	0.000435
2	-0.261143	-3.2302	0.000757
3	-0.347805	-4.3021	1.5e-05
4	-0.269948	-3.3391	0.000528
5	0.074184	0.9176	0.180135
6	0.272923	3.3759	0.000466
7	0.090709	1.122	0.131808
8	-0.250215	-3.095	0.00117
9	-0.316611	-3.9163	6.8e-05
10	-0.243043	-3.0063	0.001546
11	0.250023	3.0926	0.001179
12	0.839454	10.3835	0
13	0.219402	2.7139	0.003707
14	-0.237694	-2.9401	0.001895
15	-0.331747	-4.1035	3.3e-05
16	-0.253844	-3.1399	0.001014
17	0.059501	0.736	0.231433
18	0.213869	2.6454	0.004506
19	0.067087	0.8298	0.203966
20	-0.251807	-3.1147	0.001099
21	-0.312888	-3.8702	8e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.274566 & 3.3962 & 0.000435 \tabularnewline
2 & -0.261143 & -3.2302 & 0.000757 \tabularnewline
3 & -0.347805 & -4.3021 & 1.5e-05 \tabularnewline
4 & -0.269948 & -3.3391 & 0.000528 \tabularnewline
5 & 0.074184 & 0.9176 & 0.180135 \tabularnewline
6 & 0.272923 & 3.3759 & 0.000466 \tabularnewline
7 & 0.090709 & 1.122 & 0.131808 \tabularnewline
8 & -0.250215 & -3.095 & 0.00117 \tabularnewline
9 & -0.316611 & -3.9163 & 6.8e-05 \tabularnewline
10 & -0.243043 & -3.0063 & 0.001546 \tabularnewline
11 & 0.250023 & 3.0926 & 0.001179 \tabularnewline
12 & 0.839454 & 10.3835 & 0 \tabularnewline
13 & 0.219402 & 2.7139 & 0.003707 \tabularnewline
14 & -0.237694 & -2.9401 & 0.001895 \tabularnewline
15 & -0.331747 & -4.1035 & 3.3e-05 \tabularnewline
16 & -0.253844 & -3.1399 & 0.001014 \tabularnewline
17 & 0.059501 & 0.736 & 0.231433 \tabularnewline
18 & 0.213869 & 2.6454 & 0.004506 \tabularnewline
19 & 0.067087 & 0.8298 & 0.203966 \tabularnewline
20 & -0.251807 & -3.1147 & 0.001099 \tabularnewline
21 & -0.312888 & -3.8702 & 8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191186&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.274566[/C][C]3.3962[/C][C]0.000435[/C][/ROW]
[ROW][C]2[/C][C]-0.261143[/C][C]-3.2302[/C][C]0.000757[/C][/ROW]
[ROW][C]3[/C][C]-0.347805[/C][C]-4.3021[/C][C]1.5e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.269948[/C][C]-3.3391[/C][C]0.000528[/C][/ROW]
[ROW][C]5[/C][C]0.074184[/C][C]0.9176[/C][C]0.180135[/C][/ROW]
[ROW][C]6[/C][C]0.272923[/C][C]3.3759[/C][C]0.000466[/C][/ROW]
[ROW][C]7[/C][C]0.090709[/C][C]1.122[/C][C]0.131808[/C][/ROW]
[ROW][C]8[/C][C]-0.250215[/C][C]-3.095[/C][C]0.00117[/C][/ROW]
[ROW][C]9[/C][C]-0.316611[/C][C]-3.9163[/C][C]6.8e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.243043[/C][C]-3.0063[/C][C]0.001546[/C][/ROW]
[ROW][C]11[/C][C]0.250023[/C][C]3.0926[/C][C]0.001179[/C][/ROW]
[ROW][C]12[/C][C]0.839454[/C][C]10.3835[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.219402[/C][C]2.7139[/C][C]0.003707[/C][/ROW]
[ROW][C]14[/C][C]-0.237694[/C][C]-2.9401[/C][C]0.001895[/C][/ROW]
[ROW][C]15[/C][C]-0.331747[/C][C]-4.1035[/C][C]3.3e-05[/C][/ROW]
[ROW][C]16[/C][C]-0.253844[/C][C]-3.1399[/C][C]0.001014[/C][/ROW]
[ROW][C]17[/C][C]0.059501[/C][C]0.736[/C][C]0.231433[/C][/ROW]
[ROW][C]18[/C][C]0.213869[/C][C]2.6454[/C][C]0.004506[/C][/ROW]
[ROW][C]19[/C][C]0.067087[/C][C]0.8298[/C][C]0.203966[/C][/ROW]
[ROW][C]20[/C][C]-0.251807[/C][C]-3.1147[/C][C]0.001099[/C][/ROW]
[ROW][C]21[/C][C]-0.312888[/C][C]-3.8702[/C][C]8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191186&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.274566	3.3962	0.000435
2	-0.261143	-3.2302	0.000757
3	-0.347805	-4.3021	1.5e-05
4	-0.269948	-3.3391	0.000528
5	0.074184	0.9176	0.180135
6	0.272923	3.3759	0.000466
7	0.090709	1.122	0.131808
8	-0.250215	-3.095	0.00117
9	-0.316611	-3.9163	6.8e-05
10	-0.243043	-3.0063	0.001546
11	0.250023	3.0926	0.001179
12	0.839454	10.3835	0
13	0.219402	2.7139	0.003707
14	-0.237694	-2.9401	0.001895
15	-0.331747	-4.1035	3.3e-05
16	-0.253844	-3.1399	0.001014
17	0.059501	0.736	0.231433
18	0.213869	2.6454	0.004506
19	0.067087	0.8298	0.203966
20	-0.251807	-3.1147	0.001099
21	-0.312888	-3.8702	8e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.274566	3.3962	0.000435
2	-0.363967	-4.502	7e-06
3	-0.187095	-2.3142	0.010992
4	-0.24386	-3.0164	0.001498
5	0.075606	0.9352	0.175582
6	0.050779	0.6281	0.265439
7	-0.088549	-1.0953	0.137556
8	-0.264077	-3.2664	0.000672
9	-0.164137	-2.0303	0.022031
10	-0.309532	-3.8287	9.4e-05
11	0.196	2.4244	0.00825
12	0.719652	8.9016	0
13	-0.223996	-2.7707	0.003144
14	0.145846	1.804	0.036598
15	0.013405	0.1658	0.434261
16	0.045458	0.5623	0.287372
17	-0.04417	-0.5464	0.292811
18	-0.189968	-2.3498	0.010031
19	-0.030387	-0.3759	0.353769
20	-0.141955	-1.7559	0.040554
21	-0.135393	-1.6747	0.048016

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.274566 & 3.3962 & 0.000435 \tabularnewline
2 & -0.363967 & -4.502 & 7e-06 \tabularnewline
3 & -0.187095 & -2.3142 & 0.010992 \tabularnewline
4 & -0.24386 & -3.0164 & 0.001498 \tabularnewline
5 & 0.075606 & 0.9352 & 0.175582 \tabularnewline
6 & 0.050779 & 0.6281 & 0.265439 \tabularnewline
7 & -0.088549 & -1.0953 & 0.137556 \tabularnewline
8 & -0.264077 & -3.2664 & 0.000672 \tabularnewline
9 & -0.164137 & -2.0303 & 0.022031 \tabularnewline
10 & -0.309532 & -3.8287 & 9.4e-05 \tabularnewline
11 & 0.196 & 2.4244 & 0.00825 \tabularnewline
12 & 0.719652 & 8.9016 & 0 \tabularnewline
13 & -0.223996 & -2.7707 & 0.003144 \tabularnewline
14 & 0.145846 & 1.804 & 0.036598 \tabularnewline
15 & 0.013405 & 0.1658 & 0.434261 \tabularnewline
16 & 0.045458 & 0.5623 & 0.287372 \tabularnewline
17 & -0.04417 & -0.5464 & 0.292811 \tabularnewline
18 & -0.189968 & -2.3498 & 0.010031 \tabularnewline
19 & -0.030387 & -0.3759 & 0.353769 \tabularnewline
20 & -0.141955 & -1.7559 & 0.040554 \tabularnewline
21 & -0.135393 & -1.6747 & 0.048016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191186&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.274566[/C][C]3.3962[/C][C]0.000435[/C][/ROW]
[ROW][C]2[/C][C]-0.363967[/C][C]-4.502[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.187095[/C][C]-2.3142[/C][C]0.010992[/C][/ROW]
[ROW][C]4[/C][C]-0.24386[/C][C]-3.0164[/C][C]0.001498[/C][/ROW]
[ROW][C]5[/C][C]0.075606[/C][C]0.9352[/C][C]0.175582[/C][/ROW]
[ROW][C]6[/C][C]0.050779[/C][C]0.6281[/C][C]0.265439[/C][/ROW]
[ROW][C]7[/C][C]-0.088549[/C][C]-1.0953[/C][C]0.137556[/C][/ROW]
[ROW][C]8[/C][C]-0.264077[/C][C]-3.2664[/C][C]0.000672[/C][/ROW]
[ROW][C]9[/C][C]-0.164137[/C][C]-2.0303[/C][C]0.022031[/C][/ROW]
[ROW][C]10[/C][C]-0.309532[/C][C]-3.8287[/C][C]9.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.196[/C][C]2.4244[/C][C]0.00825[/C][/ROW]
[ROW][C]12[/C][C]0.719652[/C][C]8.9016[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.223996[/C][C]-2.7707[/C][C]0.003144[/C][/ROW]
[ROW][C]14[/C][C]0.145846[/C][C]1.804[/C][C]0.036598[/C][/ROW]
[ROW][C]15[/C][C]0.013405[/C][C]0.1658[/C][C]0.434261[/C][/ROW]
[ROW][C]16[/C][C]0.045458[/C][C]0.5623[/C][C]0.287372[/C][/ROW]
[ROW][C]17[/C][C]-0.04417[/C][C]-0.5464[/C][C]0.292811[/C][/ROW]
[ROW][C]18[/C][C]-0.189968[/C][C]-2.3498[/C][C]0.010031[/C][/ROW]
[ROW][C]19[/C][C]-0.030387[/C][C]-0.3759[/C][C]0.353769[/C][/ROW]
[ROW][C]20[/C][C]-0.141955[/C][C]-1.7559[/C][C]0.040554[/C][/ROW]
[ROW][C]21[/C][C]-0.135393[/C][C]-1.6747[/C][C]0.048016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191186&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191186&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.274566	3.3962	0.000435
2	-0.363967	-4.502	7e-06
3	-0.187095	-2.3142	0.010992
4	-0.24386	-3.0164	0.001498
5	0.075606	0.9352	0.175582
6	0.050779	0.6281	0.265439
7	-0.088549	-1.0953	0.137556
8	-0.264077	-3.2664	0.000672
9	-0.164137	-2.0303	0.022031
10	-0.309532	-3.8287	9.4e-05
11	0.196	2.4244	0.00825
12	0.719652	8.9016	0
13	-0.223996	-2.7707	0.003144
14	0.145846	1.804	0.036598
15	0.013405	0.1658	0.434261
16	0.045458	0.5623	0.287372
17	-0.04417	-0.5464	0.292811
18	-0.189968	-2.3498	0.010031
19	-0.030387	-0.3759	0.353769
20	-0.141955	-1.7559	0.040554
21	-0.135393	-1.6747	0.048016

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code